Model study of stresses in grooved tablets under diametral compression [proceedings]

The bending strength of tablets with a breaking line--Comparison of the results of an elastic and a "brittle cracking" finite element model with experimental findings

The aim of this work was to ascertain the influence of the position of the breaking line of bevel-edged tablets in a three-point bending test. Two different brands of commercially available, flat-round, bevel-edged tablets with a single central breaking line were studied. Breaking line positions tested, relative to the upper loading roll, were 0°, 22.5°, 45°, 67.5° and 90°. The breaking line faced either up- or downwards during the test. The practical results were compared with FEM results simulating similar test configurations. Tablets failed mainly across the failure plane, resulting in two tablet halves. An exception to this was found for tablets where the breaking line faced down and was positioned at an angle of 22.5° relative to the loading plane. Here the crack followed the breaking line in the centre of the tablets and only diverged towards the loading plane position at the edges of the tablets. The breaking line facing upwards resulted in a significantly higher tensile strength of the tablets compared to it facing downwards. However, with one exception, the orientation of the breaking line relative to the loading plane appeared not to affect the tensile strength values. A fully elastic FEM model indicated that both the position of the breaking line relative to the loading plane and as to whether the breaking line faced up- or downwards during the bending test would result in considerably different failure loads during practical experiments. The results also suggested that regardless of the breaking line position, when it is facing down crack propagation should start at the outer edges propagating towards the midpoint of the discs until failure occurs. Failure should hence always result in equal tablet halves, whereby the failure plane should coincide with the loading plane. Neither predictions fully reflected the practical behaviour of the tablets. Using a brittle cracking FEM model significantly larger tensile stresses for tablets with the breaking line positioned downwards at 0° or 22.5° relative to the loading plane were still predicted, but the differences between model and experimental values was greatly reduced. The remaining differences are more likely due to the inadequacy of the equation available to calculate the experimental tensile strength values. This equation cannot account for the presence of a breaking line and overestimates the thickness of the loading plane by the depth of the breaking line when in 0° or 22.5° position. If the depth of the breaking line is taken into account, the model predictions and the experimental findings are comparable. Also, in the brittle cracking FEM simulations the predicted crack propagation patterns were similar to those found in the experiments, and the model stress distributions across the lower surfaces were much more homogeneous and streamlined parallel to the loading plane. The brittle cracking model hence reflected the practicalities of the bending test more closely. The findings suggested that with the breaking line facing down fracture should always start in the centre of a tablet at its lower surface, initiated by the breaking line. Due to simultaneous development of larger stresses along the y-axis the tablet should still break into two equal halves along the loading plane, unless the position of the breaking line relative to the loading plane was 22.5°. In this case the tablet would fail by a mixed process, whereby failure would occur mainly along the breaking line, but due to simultaneous crack formation at the lower surface close to the bevel edge parallel to the loading plane the final breaking pattern would deviate from the breaking line about half-way from its centre, as seen in the practical experiments.

Theoretical investigations into the influence of the position of a breaking line on the tensile failure of flat, round, bevel-edged tablets using finite element methodology (FEM) and its practical relevance for industrial tablet strength testing

Flat, round tablets may have a breaking ("score") line. Pharmacopoeial tablet breaking load tests are diametral in their design, and industrially used breaking load testers often have automatic tablet feeding systems, which position the tablets between the loading platens of the machine with the breaking lines in random orientation to the applied load. The aim of this work was to ascertain the influence of the position of the breaking line in a diametral compression test using finite element methodology (FEM) and to compare the theoretical results with practical findings using commercially produced bevel-edged, scored tablets. Breaking line test positions at an angle of 0°, 22.5°, 45°, 67.5° and 90° relative to the loading plane were studied. FEM results obtained for fully elastic and elasto-plastic tablets were fairly similar, but they highlighted large differences in stress distributions depending on the position of the breaking line. The stress values at failure were predicted to be similar for tablets tested at an angle of 45° or above, whereas at lower test angles the predicted breaking loads were up to three times larger. The stress distributions suggested that not all breaking line angles would result in clean tensile failure. Practical results, however, did not confirm the differences in the predicted breaking loads, but they confirmed differences in the way tablets broke. The results suggest that it is not advisable to convert breaking loads obtained on scored tablets into tablet tensile strength values, and comparisons between different tablets or batches should carefully consider the orientation of the breaking line with respect to the loading plane, as the failure mechanisms appear to vary.